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Journal of Logic and Computation 1998 8(5):665-668; doi:10.1093/logcom/8.5.665
© 1998 by Oxford University Press
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Original Articles

Saturated Formulas in Full Linear Logic

MAURIZIO CASTELLAN1 and MARIO PIAZZA2

1Department of Mathematics, University of Siena Via del Capitano 15, 53100 Siena, Italy E-mail: mc6304{at}mclink.it
2Department of Philosophy (Section of Epistemology), University of Genoa Via Balbi 4, 16126 Genoa, Italy E-mail: m.piazza{at}mclink.it

In this note, we show by a proof-theoretical argument that in full linear logic the set of formulas for which contraction and weakening are admissible (the set of saturated formulas) does not coincide (up to equivalences) with the set of exponentiated formulas. This solves an open problem of Schellinx.

Keywords: Linear logic; modalities; proof-theory; sequent calculus


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